Determine the set of all vectors in R2 that are linear combinations of:
(b) (1, 2);
(c) (1, 2) and (-2, 4);
(d) (1, 2) and (0, 0);
(e) (1, 2) and (2, 1).
idk wth im supposed to say
when we have two vectors, it can be the whole set or a plane
but when do i know whether it is one or another?
#linear combination
hollow spear
trail cliffBOT
Determine the set of all vectors in R2 that are linear combinations of:
(b) (1,...
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dark nacelle
You check for linear independence. If you have two independent vectors in the plane, they span the plane. If they're dependent and one is not the zero vector, it's a line. Otherwise, it's just the zero vector.
hollow spear
ok but i suppose i have to specify what plane it is?? or not?
dark nacelle
In this case, there's only one plane since it's $\mathbb{R}^2$.
solid surgeBOT
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